Heat transport in turbulent Rayleigh-Benard convection: Effect of finite top- and bottom-plate conductivity

Abstract

We describe three apparatus, known as the large, medium, and small apparatus, used for high-precision measurements of the Nusselt number N as a function of the Rayleigh number R for cylindrical samples of fluid and present results illustrating the influence of the finite conductivity of the top and bottom plates on the heat transport in the fluid. We used water samples at a mean temperature of 40 degrees C (Prandtl number sigma = 4.4). The samples in the large apparatus had a diameter D of 49.69 cm and heights L = 116.33, 74.42, 50.61, and 16.52 cm. For the medium apparatus we had D = 24.81 cm, and L = 90.20 and 24.76 cm. The small apparatus contained a sample with D = 9.21 cm, and L = 9.52 cm. For each aspect ratio Gamma = D/L the data covered a range of a little over a decade of R. The maximum R = 10^12 with Nusselt numbers N = 600 was reached for Gamma = 0.43. Measurements were made with both Aluminum and Copper top and bottom plates of nominally identical size and shape. For the large and medium apparatus the results with Aluminum plates fall below those obtained with Copper plates, thus confirming qualitatively the prediction by Verzicco that plates of finite conductivity diminish the heat transport in the fluid. The Nusselt number N_infinity for plates with infinite conductivity was estimated by fitting simultaneously Aluminum- and Copper-plate data sets to an effective powerlaw for N_infinity multiplied by a correction factor f(X) = 1 - exp[-(aX)^b] that depends on the ratio X of the thermal resistance of the fluid to that of the plates as suggested by Verzicco. Within their uncertainties the parameters a and b were independent of Gamma for the large apparatus and showed a small Gamma-dependence for the medium apparatus. The correction was larger for the large, smaller for the medium, and negligible for the small apparatus.

arXiv comment35 pages, 11 figures. Under consideration for publication in Phys. of Fluids

References in corpus (5)

• Scaling in thermal convection: A unifying theory
• Thermal convection for large Prandtl numbers
• Heat transport by turbulent Rayleigh-B'enard Convection in cylindrical cells with aspect ratio one and less
• Heat Transport in Turbulent Rayleigh-Benard Convection
• Heat Transfer in Turbulent Rayleigh-Benard Convection below the Ultimate Regime

Cited by in corpus (32)

• Large scale dynamics in turbulent Rayleigh-Benard convection
• The unifying theory of scaling in thermal convection: The updated prefactors
• Orientation changes of the large-scale circulation in turbulent Rayleigh-Benard convection
• Comparison between two and three dimensional Rayleigh-Bénard convection
• Prandtl-, Rayleigh-, and Rossby-number dependence of heat transport in turbulent rotating Rayleigh-Benard convection
• Heat transport by turbulent Rayleigh-B'enard Convection in cylindrical cells with aspect ratio one and less
• AFiD-GPU: a versatile Navier-Stokes Solver for Wall-Bounded Turbulent Flows on GPU Clusters
• Transitions between turbulent states in rotating Rayleigh-Benard convection
• Turbulent thermal convection over rough plates with varying roughness geometries
• The Twente turbulent Taylor-Couette (T3C) facility: Strongly turbulent (multiphase) flow between two independently rotating cylinders
• The role of Stewartson and Ekman layers in turbulent rotating Rayleigh-Bénard convection
• Absense of slow transients, and the effect of imperfect vertical alignment, in turbulent Rayleigh-Benard convection
• Effect of a polymer additive on heat transport in turbulent Rayleigh-Bénard convection
• Enhanced heat transport by turbulent two-phase Rayleigh-Bénard convection
• A model of diffusion in a potential well for the dynamics of the large-scale circulation in turbulent Rayleigh-Benard convection
• Heat transport by turbulent Rayleigh-Bénard convection for $\Pra\ \simeq 0.8$ and $3\times 10^{12} \alt \Ra\ \alt 10^{15}$: Aspect ratio $\Gamma =0.50$
• Aspect ratio dependence of heat transport by turbulent Rayleigh-Bénard convection in rectangular cells
• Non-Oberbeck-Boussinesq effects in turbulent thermal convection in ethane close to the critical point
• Azimuthal asymmetries of the large-scale circulation in turbulent Rayleigh-Benard convection
• A low-dimensional model predicting geometry-dependent dynamics of large-scale coherent structures in turbulence
• Laboratory Exploration of Heat Transfer Regimes in Rapidly Rotating Turbulent Convection
• Heat transport scaling and transition in geostrophic rotating convection with varying aspect ratio
• Sidewall effects in Rayleigh-Bénard convection
• Effect of aspect-ratio on vortex distribution and heat transfer in rotating Rayleigh-Bénard convection
• The State of the Art in Hydrodynamic Turbulence: Past Successes and Future Challenges
• Thermal boundary condition studies in large aspect ratio Rayleigh-Bénard convection
• Low-dimensional model of the large-scale circulation of turbulent Rayleigh-B{é}nard convection in a cubic container
• Effect of boundary conditions in turbulent thermal convection
• Regime crossover in Rayleigh-Benard convection with mixed boundary conditions
• Effects of rotation on the bulk turbulent convection
• Effect of the Earth's Coriolis force on the large-scale circulation of turbulent Rayleigh-Benard convection
• Bounds on Rayleigh-Benard convection with general thermal boundary conditions. Part 1. Fixed Biot number boundaries